Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. #16810440 | C4 | semidirect |
| 24. #16810439 | C4 | semidirect |
| 25. #16810438 | C4 | semidirect |
| 26. C53×#362 | C4 | semidirect |
| 174. #362 | #6157 | semidirect |
| 176. C53 | #13139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#365 | 2 |
| D53⋊#362 | 2 |
| #20290863 | 2 |
| #20290536 | 2 |
| #20289781 | 2 |
| #20289761 | 2 |
| #362×D53 | 2 |
| #13139 | 53 |